Anyone can easily see that Nintendo will only ever be hardware makers.
This is obvious from the QoL platform and NX

It could expand their audience, but there's no guarantee to it at all. Worse even, Nintendos own titles could get drowned between the "mature" titles of the other consoles and their "kiddie" image, thus possibly selling even less.

Also, I find your calculations a bit flawed:

1. 40$ per third party title/60$ for Nintendo titles: I don't know the situation where you live, but here third party titles don't drop in price at all on the Wii U, or at least rarely. From my point of view here, you could keep them at a higher price. On top of that, not every Nintendo title sells for 60$ at release. So I'd say 50$ each would be more appropriate.

2. You're missing out on the digital sales on the eShop. We don't know how much they sell there but the earnings Nintendo gains there would be lost if going third party. And some of the Indies sell rather well, so this does adds quite a few millions to the balance

3. Could Nintendo still keep their 60$ pricetag for so long on consoles where most games drop their prices after a few weeks or month? Not so sure about that. Since Nintendo games are much less frontloaded than games of other companies, this might be very significant.

4. Would they still produce games from smaller series as they do now to feed their consoles? Very doubtful, just look at SEGA. This would reduce the amount of games and thus sales as a whole. The Lineup would probably be reduced to Mario Jump & Run, Zelda, Animal Crossing, Pokemon, Fire Emblem, Smash, Mario Kart and the odd other title once in a while, as they will have to concentrate on games which really make them money.

This post right here pretty much sums up the problems behind nintendo going third party. It would be great for people who only want zelda, mario and pokemon. Absolutely terrible for those of us who are fans enough to buy their consoles, enjoy many of their smaller IPs, and enjoy the projects they fund from third partys in order to bolster their library.

The profit ceiling that Nintendo could make as a Hardware maker is higher than that of a third party.

Atari went 3rd party and now a faint memory did not work out for them. 3D0 didn't work out for them 3rd party. SEGA didn't work out for them 3rd party. It seems it never works. I don't want to see Nintendo have a similar fate.

Obviously Nintendo has much stronger IP than any of those companies but ur right we have never seen a hardware manufacturer go 3rd party and have it benefit them in any meaningful way.

No, phones are a threat to handheld gaming. There's no way around that. But it's not a "lethal" threat. It's not gonna kill handhelds. It wouldn't benefit Nintendo to completely abandon handhelds and release pokemon etc. on phones (at least I don't think it would). But (I think) it does benefit Nintendo to release their home console games on other consoles, and ditch making their own hardware. I'm not really sure how I've argued that smarthphones and PCs aren't competing against handhelds?

There is no comparing Atari or 3DO nor SEGA to Nintendo.

3DO was never big ever, they never had anything close to the brand power Nintendo does. SEGA was in a financial hell and had lost nearly all their talent before they went third party. Atari also failed before they went third party. And the actual Atari never really went third party. It's more like their brand name got bought up by another publisher, and used to boost the popularity of those games. Not that that worked.

In that case wouldn't it be more beneficial for Nintendo to divert all resources to their handheld and perhaps release a Vita TV-like device for the small group of people who prefer playing on a TV instead of spreading themselves thin making games for PS/XB/PC while still trying to support their handheld?

"The small group of people who prefer to play on a TV" lol. Small compared to mobile, bigger than the group that plays on handhelds though.

But no, it wouldn't. Nintendo can/ will only release on Mario Kart on heir next handheld. That might sell 10 million or something. Now what would happen to the team that makes home console MKs? If they do what you say, focus all effort on their handheld, those people will have to work on something else, which is basically guaranteed to not do as well as a multiplat Mario Kart would do.

How about a middle ground? The smaller Nintendo titles (FE, etc. you know what I mean) could go to their handheld, but they'd release thr big titles, the ones that are likely to take off as multiplat games, and that normally also get one handheld release (MK, 3D Mario, Zelda, SSB etc.) could be multiplat home console games. That way they'd focus more on their handheld than they do now, and only release the occasional huge titles for home consoles. The good thing about this is that it allows Nintendo to spread their resources however they like. They no longer need to worry about droughts on their home console, so they can release smaller titles on their handhelds we're they're more likely to do well than on their home consoles, but rake in the profits from the huge titles like MK etc.

Maybe in that scenario an alliance with Microsoft would be beneficial to both parties.

I don't know if MS really has their heart in this XBox thing after this cycle, and that way Nintendo could basically make the hardware and still operate as they currently do, just with MS' backing.

I think what MS really basically wants is just their OS on the device ... so let them have it.

Honestly back in 2000 Nintendo should've just agreed to allow Windows or some watered down form of it like the Dreamcast had rather than having to deal with two conglomerate competitors. It was just never a really good situation for Nintendo to get themselves into. Basically they bet the farm on MS failing out right, but they didn't, and they got stuck into a three horse race that they wanted no part of.